Universität Osnabrück, Graduiertenkolleg Mikrostruktur oxidischer

GRADUIERTENKOLLEG MIKROSTRUKTUR OXIDISCHER KRISTALLE 25
Computer simulations of defects in KNbO3 and KTaO3
Beginn des Projekts: 01.02.1997
Ende des Projekts: 31.03.1998
Dr. Roberts Eglitis (Postdoktorand)
Betreuer: Prof. Dr. G. Borstel
Zusammenfassung
Semi-empirical Hartree-Fock calculations using the intermediate neglect of differential overlapp
(INDO) method, for self-ordered cubic symmetry clusters of seven Nb ions in KTaO3 are performed with the
aim of verifying the cluster model [1] of second component-induced phase transitions in ferroelectric perovskite
matrices. It is shown that such a seven-particle cluster in KTaO3:Nb has two types of quasidegenerate states of
different nature. Namely, the state with the equilibrium full-symmetric dilatation and off-center displacements in
[111]-directions of the central Nb-ion in the cluster, and the state with the equilibrium full-symmetric compression
without any off-center effect. The consequencies of such cluster structures on the multi-well potential are
discussed. In particular, an avalanche-like behaviour of the temperature dependence of the ferroelectric order
parameter is obtained. The results of semi-empirical INDO calculations of a seven-impurities cluster of Nb-ions
in KTaO3 confirm the key assumptions of the cluster model of induced phase transitions.
The LMTO and INDO methods are used for a supercell study of F centers in cubic and orthorhombix
ferroelectric KNbO3 crystals. Two electrons are found to be considerably delocalized even in the ground state
of the defect. The absorption energies are calculated by means of the INDO method using the ∆SCF scheme
after a relaxation of atoms surrounding the F center. As an example of another type of point defect in perovskite,
an isolated Li impurity in KTaO3 as well as interacting Li pairs are considered in the supercell approach. The
off-center Li displacement, reorientational energy barriers and the lattice relaxation around impurities are calculated.
The results are compared with those obtained earlier within the shell model, revealing the relaxation pattern
somehow different from the shell model estimations.
We used INDO method for large unit cell calculations of hole polarons bound to a cation vacancy in
partly covalent perovskite KNbO3. In KNbO3 we predict the existence of one-site and two site (molecular) polarons
with close absorption energies ∼ 1 eV.
Ergebnisse
The exploration of the Nb-clusters in KTaO3 was performed using the periodic LUC method, as it is implemented
in the updated CLUSTERD computer code [I,II,2,3]. In order to calculate the Nb clusters in KTaO3, we
replaced in our 4×4×4 times extended unit cell, containing 320 atoms, seven Ta atoms by seven Nb atoms. After
this, in order to find the energy minima of Nb clusters in KTaO3, we allowed to six Nb atoms to relax towards
the central Nb atom. The results of our calculations show that for six Nb atoms shifted symmetrically towards
the central Nb atom by 0.187 Å, the total energy per LUC is lowered by 0.088 eV. Moreover, the outward uniform
displacement of six Nb atoms from the central Nb by 0.073 Å is also favorable and lowers the energy by
approximately 0.03 eV. In the case, when 6 Nb atoms are shifted outwards from the central Nb atom, the central
Nb-atom moves off-center from central position in the [111] direction by 0.27 Å, further lowering the total energy
of system by 0.09 eV. These configurations correspond to a ground-state vibronic multiplet. The Nb atom
reveals also an instability in the [100] direction. The shift of the central Nb ion along the [100] direction by
0.192 Å lowers the cluster energy additionally by 0.056 eV in the same case when six Nb atoms are shifted
outwards from the central Nb atom. The total cluster-structure induced energy lowering in the ground state,
which corresponds to the situation when six Nb atoms are symmetrically shifted in the direction from the center
of the Nb cluster, and the central Nb atom is off-center in the [111] direction is 0.12 eV [III]. According